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Register a new userGenerating Event Triggers Based on Hilbert-Huang Transform and Its Application to Gravitational-Wave Data
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We present a new event trigger generator based on the Hilbert-Huang transform, named EtaGen ($eta$Gen). It decomposes a time-series data into several adaptive modes without imposing a priori bases on the data. The adaptive modes are used to find transients (excesses) in the background noises. A clustering algorithm is used to gather excesses corresponding to a single event and to reconstruct its waveform. The performance of EtaGen is evaluated by how many injections in the LIGO simulated data are found. EtaGen is viable as an event trigger generator when compared directly with the performance of Omicron, which is currently the best event trigger generator used in the LIGO Scientific Collaboration and Virgo Collaboration.
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The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.
With the advent of gravitational wave astronomy, techniques to extend the reach of gravitational wave detectors are desired. In addition to the stellar-mass black hole and neutron star mergers already detected, many more are below the surface of the noise, available for detection if the noise is reduced enough. Our method (DeepClean) applies machine learning algorithms to gravitational wave detector data and data from on-site sensors monitoring the instrument to reduce the noise in the time-series due to instrumental artifacts and environmental contamination. This framework is generic enough to subtract linear, non-linear, and non-stationary coupling mechanisms. It may also provide handles in learning about the mechanisms which are not currently understood to be limiting detector sensitivities. The robustness of the noise reduction technique in its ability to efficiently remove noise with no unintended effects on gravitational-wave signals is also addressed through software signal injection and parameter estimation of the recovered signal. It is shown that the optimal SNR ratio of the injected signal is enhanced by $sim 21.6%$ and the recovered parameters are consistent with the injected set. We present the performance of this algorithm on linear and non-linear noise sources and discuss its impact on astrophysical searches by gravitational wave detectors.
The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals out of the box, handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.
Through numerical simulations, it is predicted that the gravitational waves (GWs) reflect the characteristics of the core-collapse supernova (CCSN) explosion mechanism. There are multiple GW excitation processes that occur inside a star before its explosion, and it is suggested that the GWs originating from the CCSN have a mode for each excitation process in terms of time-frequency representation. Therefore, we propose an application of the Hilbert-Huang Transform (HHT), which is a high-resolution time-frequency analysis method, to analyze these GW modes for theoretically probing and increasing our understanding of the explosion mechanism. The HHT defines frequency as a function of time, and is not bound by the trade-off between time and frequency resolutions. In this study, we analyze a gravitational waveform obtained from a three-dimensional general-relativistic CCSN model that showed a vigorous activity of the standing-accretion-shock-instability (SASI). We succeed in extracting the SASI induced GWs with high resolution on a time-frequency representation using the HHT and we examine their instantaneous frequencies.
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
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